CODEWITHSUNDEEP
rnon-linear-regression
ck24501
ck24501

Reputation: 17

Errors in nls() - singular gradient or NaNs produced

I am trying to fit my photosynthesis data to a nls function, which is a nonrectangular hyperbola function. So far, I have some issues with getting the right start value for nls and, therefore, I am getting a lot of errors such as 'singular gradient ', 'NaNs produced', or 'step factor 0.000488281 reduced below 'minFactor' of 0.000976562'. Would you please give some suggestions for finding the best starting values? Thanks in advance!

The codes and data are below:

#Dataframe
PPFD <- c(0,0,0,50,50,50,100,100,100,200,200,200,400,400,400,700,700,700,1000,1000,1000,1500,1500,1500)
Cultivar <- c(-0.7,-0.8,-0.6,0.6,0.5,0.8,2.0,2.0,2.3,3.6,3.7,3.7,5.7,5.5,5.8,9.7,9.6,10.0,14.7,14.4,14.9,20.4,20.6,20.9)
NLRC <-data.frame(PPFD,Cultivar)

#nls regression
reg_nrh <- nls(Cultivar ~ (1/(2*Theta))*(AQY*PPFD+Am-sqrt((AQY*PPFD+Am)^2-4*AQY*Theta*Am*PPFD))-Rd, data = NLRC, start=list(Am = max(NLRC$Cultivar)-min(NLRC$Cultivar), AQY = 0.05, Rd=-min(NLRC$Cultivar), Theta = 1))

#estimated parameters for plotting
Amnrh <- coef(reg_nrh)[1]
AQYnrh <- coef(reg_nrh)[2]
Rdnrh <- coef(reg_nrh)[3]
Theta <- coef(reg_nrh)[4]

#plot
plot(NLRC$PPFD, NLRC$Cultivar, main = c("Cultivar"), xlab="", ylab="", ylim=c(-2,40),cex.lab=1.2,cex.axis=1.5,cex=2)+mtext(expression("PPFD ("*mu*"mol photons "*m^-2*s^-1*")"),side=1,line=3.3,cex=1.5)+mtext(expression(P[net]*" ("*mu*"mol "*CO[2]*" "*m^-2*s^-1*")"),side=2,line=2.5,cex=1.5)

#simulated value
ppfd = seq(from = 0, to = 1500)
pnnrh <- (1/(2*Theta))*(AQYnrh*ppfd+Amnrh-sqrt((AQYnrh*ppfd+Amnrh)^2-4*AQYnrh*Theta*Amnrh*ppfd))- Rdnrh
lines(ppfd, pnnrh, col="Green")

Upvotes: 1

Views: 297

Answers (1)

G. Grothendieck
G. Grothendieck

Reputation: 270448

If we

  1. take the maximum of 0 and the expression within the sqrt to avoid taking negative square roots
  2. fix Theta at 0.8
  3. use lm to get starting values for AQY and Am

then it converges

Theta <- 0.8
fm <- lm(Cultivar ~ PPFD, NLRC)
st <- list(AQY = coef(fm)[[2]], Rd = -min(NLRC$Cultivar), Am = coef(fm)[[1]])
fo <- Cultivar ~ 
  (1/(2*Theta))*(AQY*PPFD+Am-sqrt(pmax(0, (AQY*PPFD+Am)^2-4*AQY*Theta*Am*PPFD)))-Rd
reg <- nls(fo, data = NLRC, start = st)

deviance(reg)  # residual sum of squares
## [1] 5.607943

plot(Cultivar ~ PPFD, NLRC)
lines(fitted(reg) ~ PPFD, NLRC, col = "red")

(continued after image) screenshot

Note that the first model below has only two parameters yet has lower residual sum of squares (lower is better).

reg2 <- nls(Cultivar ~ a * PPFD^b, NLRC, start = list(a = 1, b = 1))
deviance(reg2)
## [1] 5.098796

These have higher residual sum of squares but do have the advantage that they are very simple.

deviance(fm) # fm defined above
## [1] 6.938648

fm0 <- lm(Cultivar ~ PPFD + 0, NLRC) # same as fm except no intercept
deviance(fm0)
## [1] 7.381632

Upvotes: 1

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